Price equation

In the theory of evolution and natural selection, the Price equation (also known as Price's equation or Price's theorem) describes how a trait or allele changes in frequency over time. The equation uses a covariance between a trait and fitness, to give a mathematical description of evolution and natural selection. It provides a way to understand the effects that gene transmission and natural selection have on the frequency of alleles within each new generation of a population. The Price equation was derived by George R. Price, working in London to re-derive W.D. Hamilton's work on kin selection. Examples of the Price equation have been constructed for various evolutionary cases. The Price equation also has applications in economics. It is important to note that the Price equation is not a physical or biological law. It is not a concise or general expression of experimentally validated results. It is rather a purely mathematical relationship between various statistical descriptors of population dynamics. It is mathematically valid, and therefore not subject to experimental verification. In simple terms, it is a mathematical restatement of the expression "survival of the fittest" which is actually self-evident, given the mathematical definitions of "survival" and "fittest". The Price equation shows that a change in the average amount of a trait in a population from one generation to the next () is determined by the covariance between the amounts of the trait for subpopulation and the fitnesses of the subpopulations, together with the expected change in the amount of the trait value due to fitness, namely : Here is the average fitness over the population, and and represent the population mean and covariance respectively. 'Fitness' is the ratio of the average number of offspring for the whole population per the number of adult individuals in the population, and is that same ratio only for subpopulation . If the covariance between fitness () and trait value () is positive, the trait value is expected to rise on average across population .